President Barack Obama gestures as he speaks during the last stop on his Bus Tour promoting his jobs plan, Wednesday, at a Chesterfield County fire station in Richmond, Va.

Steve Helber/AP

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Washington — In a rebuff to President Obama’s jobs strategy, Senate Republicans late Thursday blocked a $35 billion bill to avoid or reverse layoffs of teachers, firefighters, and police – setting up an ongoing dispute for the 2012 election cycle.

The vote marked the first attempt by Senate Democrats to pass a scaled-down version of the president’s $447 billion jobs plan, which the Senate rejected on Oct. 12.

But all will have to pass the 60-vote threshold in the Senate. With Republicans unanimously opposed – and a few moderate Democrats willing to break ranks – it’s a formidable hurdle.

“Our fight isn’t over,” said President Obama in a statement after the vote. “We will keep working with Congress to bring up the American Jobs Act piece by piece, and give Republicans another chance to put country before party and help us put the American people back to work.”

Senate Republicans dubbed the Teachers and First Responders Back to Work bill a “bailout” for states and public service workers, at the expense of creating jobs in the private sector. The 0.5 percent tax hike for incomes greater than $1 million that Democrats proposed to pay for the measure would hit small business owners, discouraging investment and hiring, they said.

Sen. Marco Rubio (R) of Florida, a tea party favorite, said that the federal government can’t afford “another bailout of local governments,” while running its own massive debt. “We can’t afford stimulus 2.0,” he said, in a video statement.

It’s an ideological divide that both parties seem eager to carry into the 2012 elections.

“Republicans unanimously blocked a bill that would have kept 400,000 teachers in the classroom and first responders on the job because they refuse to ask millionaires to pay their fair share,” said Senator Reid, in a statement after the vote.

The Senate also blocked a proposal by Senate Republicans to repeal a 3 percent tax to government contractors, set to take effect in 2013. Republicans propose offsetting costs of the repeal by $30 billion in unspecified spending cuts.

A similar measure in Obama’s jobs plan would have delayed implementation of the tax, but not repealed it. Ironically, the tax was first passed by a GOP-controlled Congress in 2006 as a bid to ensure tax compliance, but never implemented by majorities in either party. The White House plan proposed offsetting costs of the delay with permanent tax hikes.

The GOP measure failed to meet the 60-vote target, 57 to 43. Ten Democrats – all but three of whom are up for reelection in 2012 – voted with all Republicans in favor of repeal.

The GOP-controlled House proposes taking up a similar measure to repeal this tax hike when the House returns to Washington next week. The Senate is effectively on a recess until Oct. 31.

“House Republicans are serious about making sure America is a place for opportunity, and that is why we are focused on ideas supported by the president and Democrats in Congress that will create jobs and return economic growth," said House majority leader Eric Cantor (R) of Virginia, in a statement on Friday. "Next week, the House will vote to repeal the 3 percent withholding rule to remove unnecessary costs on businesses already facing uncertainty."